How to generate a normal map from a bump map?
In Cycles, you can do like this :


create a plane and unwrap it
add a material to it, like this in the node editor, from left to right : UV input node, your source image, a bump map vector, connected to the displacement of the material.
The result image (on the right) is added and selected in order to be baked to.




Now go to the render panel, in the bake section : choose bake type = "Normal", and click "bake".
Here is the result :



The blend file :